Whose CommonWealth Is It Anyway?

Real-estate investors Barry Portnoy and son Adam are facing an activists' challenge over CommonWealth REIT, which they run via another firm.

Over the years, real-estate investors Barry Portnoy and son Adam have usually come out on top in corporate clashes. But their latest battle, over the future of CommonWealth REIT, could be their toughest yet. If the activists that the Portnoys face have their way, shareholders could see a 30% pop in the stock—or more.

CommonWealth (ticker: CWH), a real-estate investment trust with 440 office properties in second-tier cities from the East Coast to Hawaii, owns $7.8 billion worth of commercial real estate. Even subtracting...